A 10-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle , there are three forces acting on the weight, as shown in Figure. N is called the normal force and it acts in the direction perpendicular to the bench. F is the force due to friction that holds the weight on the bench. If the weight does not move, then the sum of these three forces is 0. Find the magnitude of N and the magnitude of F .
A) lb, lb
B) lb, lb
C) lb, lb
D) lb, lb
E) lb, lb

Question

A 10-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle  , there are three forces acting on the weight, as shown in Figure. N is called the normal force and it acts in the direction perpendicular to the bench. F is the force due to friction that holds the weight on the bench. If the weight does not move, then the sum of these three forces is 0. Find the magnitude of N and the magnitude of F .    ​
A) lb, lb 
B) lb, lb 
C) lb, lb 
D) lb, lb 
E) lb, lb

Quizplus · Accepted Answer

Since the weight is not moving, the sum of the forces in the x and y direction must be zero. In the y direction, the normal force and weight force cancel each other out: 
N = mg = 10 lb 
In the x direction, the force due to friction must be equal and opposite to the component of the weight force parallel to the bench: 
F = mg*sin(11ebf5ef_bb76_19ce_95d1_4d0e7406a176_TBX9354_11) = 1.83 lb 
Therefore, the magnitude of N is 10 lb and the magnitude of F is 1.83 lb. Choice D is the only option that matches these values.

A 10-Pound Weight Is Lying on a Sit-Up Bench at the Gym